Question

triangle nop is formed by connecting the midpoints of the side of triangle klm. the lengths of the sides of triangle nop find the perimeter of triangle klm. figures not necessarily drawn to scale. image of triangle klm with midpoints o, n, p forming triangle nop, with side lengths 9, 5, 8 in triangle nop answer attempt 1 out of 2 submit answer button

Explanation:

Step1: Use the mid - segment theorem

The mid - segment theorem states that the length of a mid - segment of a triangle (a segment connecting the midpoints of two sides of a triangle) is half the length of the third side.
If \(OP = 9\), then the side of \(\triangle KLM\) parallel to \(OP\) (say \(KL\)) has length \(2\times9=18\).
If \(ON = 5\), then the side of \(\triangle KLM\) parallel to \(ON\) (say \(MK\)) has length \(2\times5 = 10\).
If \(PN=8\), then the side of \(\triangle KLM\) parallel to \(PN\) (say \(ML\)) has length \(2\times8=16\).

Step2: Calculate the perimeter of \(\triangle KLM\)

The perimeter \(P\) of a triangle is the sum of the lengths of its sides.
\(P=18 + 10+16\)
\(P=(18 + 10)+16=28 + 16=44\)

Answer:

\(44\)